Survival and stationary distribution of a SIR epidemic model with stochastic perturbations
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摘要
In this paper, the dynamics of a SIR epidemic model is investigated. First, we show that the system admits a unique positive global solution starting from the positive initial value. Then, when R0>1, we show that the stochastic model has a stationary distribution under certain parametric restrictions. In particular, we show that random effects may lead the disease to extinction in scenarios where the deterministic model predicts persistence. When R0⩽1, a result on fluctuation of the solution around the disease-free equilibrium of deterministic system is established under suitable conditions. Finally, numerical simulations are carried out to illustrate the theoretical results.
论文关键词:Stochastic SIR epidemic model,Stationary distribution,Itô formula,Extinction
论文评审过程:Available online 20 July 2014.
论文官网地址:https://doi.org/10.1016/j.amc.2014.06.100